\(J\)-symmetric factorizations and algebraic Riccati equations. (English) Zbl 0994.47021
Dijksma, A. (ed.) et al., Recent advances in operator theory. The Israel Gohberg anniversary volume. Proceedings of the international workshop on operator theory and its applications, IWOTA-98, Groningen, Netherlands, June 30-July 3, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 124, 319-360 (2001).
Authors’ summary: This paper discusses two interrelated topics: minimal \(J\)-symmetric factorizations of rational matrix functions and the algebraic Riccati equation. In particular, necessary and sufficient conditions are presented for the existence of a complete set of minimal \(J\)-symmetric factorizations of a selfadjoint rational matrix function with constant signature. For the algebraic Riccati equation, first result describes the connection between the Hermitian solutions, \(J\)-symmetric factorizations of the Popov function and generalized Bezoutians. Then, necessary and sufficient conditions are given to have a complete set of solutions. Both the continuous and discrete algebraic Riccati equation are treated.
For the entire collection see [Zbl 0966.00029].
For the entire collection see [Zbl 0966.00029].
MSC:
| 47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 15A24 | Matrix equations and identities |
| 47B50 | Linear operators on spaces with an indefinite metric |
| 49N05 | Linear optimal control problems |
| 93B36 | \(H^\infty\)-control |
